Discontinuous Galerkin methods for the Stokes equations using divergence‐free approximations

This is the pre-peer reviewed version of the following article: Montlaur, A.; Fernandez, S.; Huerta, A. Discontinuous Galerkin methods for the Stokes equations using divergence-free approximations. "International journal for numerical methods in fluids", Juliol 2008, vol. 57, num. 9, p. 1071-1092., which has been published in final form at http://www3.interscience.wiley.com/journal/117953707/abstract?CRETRY=1&SRETRY=0

[1]  Bernardo Cockburn,et al.  Hybridized globally divergence-free LDG methods. Part I: The Stokes problem , 2005, Math. Comput..

[2]  David F. Griffiths,et al.  An approximately divergence‐free 9‐node velocity element (with variations) for incompressible flows , 1981 .

[3]  Igor Mozolevski,et al.  Discontinuous Galerkin finite element approximation of the two-dimensional Navier-Stokes equations in stream-function formulation , 2006 .

[4]  Douglas N. Arnold,et al.  Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems , 2001, SIAM J. Numer. Anal..

[5]  Ohannes A. Karakashian,et al.  A Nonconforming Finite Element Method for the Stationary Navier--Stokes Equations , 1998 .

[6]  Antonio Huerta,et al.  High-order accurate time-stepping schemes for convection-diffusion problems , 2000 .

[7]  Fridolin Okkels,et al.  Applications of topology optimization in the design of micro- and nanofluidic systems , 2005 .

[8]  P. Hansbo,et al.  A finite element method for the simulation of strong and weak discontinuities in solid mechanics , 2004 .

[9]  I. Babuska The Finite Element Method with Penalty , 1973 .

[10]  Peter Hansbo,et al.  Piecewise divergence‐free discontinuous Galerkin methods for Stokes flow , 2006 .

[11]  Guido Kanschat,et al.  A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier–Stokes Equations , 2007, J. Sci. Comput..

[12]  Bernardo Cockburn,et al.  Discontinuous Galerkin Methods for Computational Fluid Dynamics , 2004 .

[13]  Max Gunzburger,et al.  Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice, and Algorithms , 1989 .

[14]  Bernardo Cockburn,et al.  Incompressible Finite Elements via Hybridization. Part I: The Stokes System in Two Space Dimensions , 2005, SIAM J. Numer. Anal..

[15]  P. Hansbo,et al.  CHALMERS FINITE ELEMENT CENTER Preprint 2000-06 Discontinuous Galerkin Methods for Incompressible and Nearly Incompressible Elasticity by Nitsche ’ s Method , 2007 .

[16]  D. Arnold An Interior Penalty Finite Element Method with Discontinuous Elements , 1982 .

[17]  Ohannes A. Karakashian,et al.  Piecewise solenoidal vector fields and the Stokes problem , 1990 .

[18]  Andrea Toselli,et al.  HP DISCONTINUOUS GALERKIN APPROXIMATIONS FOR THE STOKES PROBLEM , 2002 .

[19]  P. Raviart,et al.  Conforming and nonconforming finite element methods for solving the stationary Stokes equations I , 1973 .

[20]  P. Hansbo,et al.  An unfitted finite element method, based on Nitsche's method, for elliptic interface problems , 2002 .

[21]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.